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What to look for: the Higgs-to-gamma-gamma branching ratio

There’s a lot of press building up to the Higgs announcement at CERN in just a few hours, and you’ll have Aidan’s live-blog for the play-by-play commentary. I just wanted to squeeze in more chatter about what to look for in the talks besides the usual “oh look how many sigmas we have.”

Since we’re all friends here, I’ll be candid and say that many physicists have taken the existence of a 125 GeV-ish Higgs-like particle as a foregone conclusion—in large part because any alternative would be even more dramatic. (Recall: the Standard Model is begging for there to be a Higgs.) Whether the evidence for the Higgs is just above or just below the magic 5-sigma “discovery” threshold won’t change anything other than how much champagne Aidan will be drinking.

But that shouldn’t deter you from tuning into the 3am EST webcast. Besides getting a chance to see some famous faces in the audience, the thing to look for are hints that there’s actually more to the Higgs than the Standard Model. As described very nicely at Resonaances, the 2011 LHC data presented last December suggested that the Higgs (if it’s there) decays into photons slightly more often than the Standard Model predicts. Could this be a hint that there’s exciting (and unexpected) new physics right around the corner?

Let’s back up a little bit. Before we can talk about how the Higgs decays, we have to talk about how it’s produced at the LHC. The two main mechanisms are called gluon fusion and vector boson fusion (where the vector boson V can be a Z or W):

The gluon fusion diagram dominates at the LHC since there are plenty of high energy gluons in a multi-TeV proton beam. Note that the loop of virtual top quarks is required since the Higgs has no direct coupling to gluons (it’s not colored); the top is a good choice since it has a large coupling to the Higgs (which is why the top is so heavy). As an exercise, use the Standard Model Feynman rules to draw other Higgs production diagrams.

Once you have a Higgs, you can look at the different ways it can decay. The photon-photon final state is very rare, but particularly intriguing because the Higgs doesn’t have electric charge and photons don’t have mass—so these particles don’t tend to talk to each other. In fact, such a Higgs-photon-photon interaction only occurs when mediated by virtual particles like the top and W:

Why these diagrams? They’re heavy enough to have a large coupling to the Higgs and also charged so they can emit photons. (Exercise: draw the other W boson diagram contributing to h to γγ.) In fact, the W diagram is about 5 times larger than the top diagram.

The great thing about loop diagrams is that any particle (with electric charge and coupling to the Higgs) can run in the loop. You can convince yourself that other Standard Model particles don’t make big contributions to h → γγ, but—and here’s the good part—if there are new particles beyond the Standard Model, they could potentially push the h → γγ rate larger than the Standard Model prediction. This is what we’re hoping.

What to look for: keep an eye out for a measurement of the h → γγ cross section (a measurement of the rate). Cross sections are usually denoted by σ. Because we don’t care so much about the actual number but rather its difference from the Standard Model, what is usually presented is a ratio of the observed cross section to the Standard Model cross section: σ/σ(SM). If this ratio is one within uncertainty, then things look like the Standard Model, but otherwise (and hopefully) things are much more interesting.

The outlook on the eve of ‘the announcement’

Given the assumption that there indeed is a particle at 125-ish GeV that does all the great things that the Standard Model Higgs should do, we would like to ask whether or not this is really the Standard Model (SM) Higgs, or whether it is some other Higgs-like state that may have different properties. In particular, is it possible that this particle talks to the rest of the Standard Model with slightly different strengths than the SM Higgs? And maybe, if we really want to push our luck, could this more exotic Higgs-like particle push the h → γγ rate to be larger than expected?

To answer this question, we don’t want to restrict ourselves to any one specific model of new physics, we’d rather be as general as possible. One way to do this is to use an “effective theory” that parameterizes all of the possible couplings of the “Higgs” to Standard Model particles. Here’s what one such effective theory looks like in sloppy handwriting:

Don’t worry, you don’t have to know what these all mean, but just for fun you can compare to this famous expression. The parameters here are the variables labelled a, b, c, and d. Of these, the two important ones to consider are a, which controls the Higgs coupling to two W bosons, and c, which controls the Higgs coupling to fermions (like top quarks). The Standard Model corresponds to a = c = 1.

Now we can start playing an interesting game:

If we increase the coupling a of the Higgs to W bosons, then we increase the rate for h → γγ via the W loop above.

If, on the other hand, we increase the coupling c of the Higgs to the top quark, then we increase the rate of h → γγ via the top quark loop above.

Thus the observation of a larger-than-expected rate for h → γγ could point to either a or c >1 (or both). How would we distinguish between these? Well, note that (see the production diagrams above):

If the a (Higgs to W) coupling were enhanced, then we would also expect an enhancement in the “vector boson fusion” rate for Higgs production. When the Higgs is produced this way, you can [with some efficiency] tag the quark remnants and say that the Higgs was produced through vector boson fusion.

On the other hand, if the c (Higgs to top) coupling were enhanced, then we would also expect an enhancement in the “gluon fusion” rate for Higgs production.

Thus we have some handle for where we could fit new physics to explain a possible h → γγ excess. (Again, by “excess” we mean relative to the expected production in the Standard Model.)

Here’s a quick plot of where we stand currently, including recent results from Moriond, from 1202.3697, I refer experts to that paper for further details and plots:

(There are many similar plots out there—some by good friends of mine—I apologize for not providing a more complete reference list… the Higgs seminar is only a few hours away!) The green/yellow/gray blobs are the 1,2,3 sigma confidence regions for the parameters a and c above. The red and blue lines are ATLAS and CMS exclusions. The reason why there are two green blobs is that there is a choice for the sign of c, this corresponds to whether the Higgs-top loops interfere constructively or destructively with the Higgs-W loops. For more details, see this Resonaances post.

The plot above includes the latest LHC data (Moriond, pre-ICHEP) as well as the so-called “electroweak precision observables” which tightly constrain the effects of virtual particles on the Standard Model gauge bosons. These are the blobs to keep an eye on—the lines indicate the Standard Model point a=c=1. If the blob continues to creep away from this point, then there will be good reason to expect exciting new physics beyond the Higgs… and that’s what makes it worth tuning in at 3am.

Do these studies consider to give the top a different status that the rest of the quarks, or they simply use a parameter to control all the fermion couplings? It seems to me that the top deserves its own coefficient, and fermiophobia should be parametrised in two categories, top-phobia on one side, and all the other fermions in other… I am ok with having a single parameter for the other fermions, at least for a start

For us numerologists, the top quark fixes all the typical scales of the other yukawas, via Koide waterfall (the requiriment that each sequence of three quarks meets Koide equation). A waterfall along three generations of quarks asking the up quark to be zero has five discrete solutions, and from them it can be singled out this one:

Of course, if we put the real masses of t and b we get more accurate values of c and s, but I like this one because it only uses one free parameter, the mass of the top.

Yep, I have put y_t=1. And this is a point that even normal physicists should consider in order to give the top a special role in all these scannings of parameter spaces. Its yukawa is 0.995 and one sigma compatible with unity.